00:02
All right, so we're looking to make a hypothesis test on the average weight loss for a group.
00:10
So we're told that the sample size is 7.
00:15
The mean weight loss, so d bar, the difference would be negative 1 .6.
00:21
And we're told the sample standard deviation of that difference is 0 .5.
00:25
And these are in pounds.
00:27
And we're going to test at the alpha of 0 .01.
00:32
That's going to be our level of significance.
00:34
So let's state our hypotheses.
00:36
So our null hypothesis is that the difference is zero.
00:41
And the alternative hypothesis is that the difference is less than zero because we're testing the claim that the diet is effective in reducing weight.
00:51
So we'd want the average weight loss, like the weight to go down to be negative.
00:57
So that's our null or our alternative hypothesis.
01:01
So, and to give a picture of this, here's our approximately normal distribution, and we have our t score here of zero.
01:13
And we're going to do exclusively on the left because we're looking just in the one direction.
01:19
It's called a one -tailed test.
01:20
So we're going to have some, you want to have our t score, we'll put t -t star, we'll say, it's such that we want to know what this error to the left of it is.
01:33
And this is going to be our p value, and we are going to read, let me write this out, we're going to reject h -0 if our p value is less than the alpha 0 .01.
02:00
And we're also going to test it at another significance level, i think at the end of the statement, we're also told to test it against the alpha 0 .05, but once we answer it for this one, it'll be the same here.
02:11
All right, let's go ahead and do this.
02:13
So our t statistic is calculated as the mean difference divided by the standardvation of the difference divided by the square of the sample size...